Handbook on Modelling for Discrete Optimization

1. Front Matter

   Pages i-xxii

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2. Methods

   1. Front Matter

      Pages 1-1

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   2. The Formulation and Solution of Discrete Optimisation Models

      • H. Paul Williams

      Pages 3-38

   3. Continuous Approaches for Solving Discrete Optimization Problems

      • Panos M Pardalos, Oleg A Prokopyev, Stanislav Busygin

      Pages 39-60

   4. Logic-Based Modeling

      • John N Hooker

      Pages 61-102

   5. Modelling for Feasibility - the Case of Mutually Orthogonal Latin Squares Problem

      • Gautam Appa, Dimitris Magos, Ioannis Mourtos, Leonidas Pitsoulis

      Pages 103-127

   6. Network Modelling

      • Douglas R. Shier

      Pages 129-149

   7. Modeling and Optimization of Vehicle Routing and Arc Routing Problems

      • Jean-Francois Cordeau, Gilbert Laporte

      Pages 151-191

3. Applications

   1. Front Matter

      Pages 193-193

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   2. Radio Resource Management

      • Katerina Papadaki, Vasilis Friderikos

      Pages 195-225

   3. Strategic and Tactical Planning Models for Supply Chain: An Application of Stochastic Mixed Integer Programming

      • Gautam Mitra, Chandra Poojari, Suvrajeet Sen

      Pages 227-264

   4. Logic Inference and a Decomposition Algorithm for the Resource-Constrained Scheduling of Testing Tasks in the Development of New Pharmaceutical and Agrochemical Products

      • Christos T. Maravelias, Ignacio E. Grossmann

      Pages 265-289

   5. A Mixed-Integer Nonlinear Programming Approach to the Optimal Planning of Offshore Oilfield Infrastructures

      • Susara A. van den Heever, Ignacio E. Grossmann

      Pages 291-315

   6. Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches

      • Michael C. Ferris, Robert R. Meyer, Warren D’Souza

      Pages 317-340

   7. Multiple Hypothesis Correlation in Track-to-Track Fusion Management

      • Aubrey B Poore, Sabino M Gadaleta, Benjamin J Slocumb

      Pages 341-371

   8. Computational Molecular Biology

      • Giuseppe Lancia

      Pages 373-425

4. Back Matter

   Pages 427-431

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The primary reason for producing this book is to demonstrate and commu­ nicate the pervasive nature of Discrete Optimisation. It has applications across a very wide range of activities. Many of the applications are only known to specialists. Our aim is to rectify this. It has long been recognized that ''modelling" is as important, if not more important, a mathematical activity as designing algorithms for solving these discrete optimisation problems. Nevertheless solving the resultant models is also often far from straightforward. Although in recent years it has become viable to solve many large scale discrete optimisation problems some problems remain a challenge, even as advances in mathematical methods, hardware and software technology are constantly pushing the frontiers forward. The subject brings together diverse areas of academic activity as well as di­ verse areas of applications. To date the driving force has been Operational Re­ search and Integer Programming as the major extention of the well-developed subject of Linear Programming. However, the subject also brings results in Computer Science, Graph Theory, Logic and Combinatorics, all of which are reflected in this book. We have divided the chapters in this book into two parts, one dealing with general methods in the modelling of discrete optimisation problems and one with specific applications. The first chapter of this volume, written by Paul Williams, can be regarded as a basic introduction of how to model discrete optimisation problems as Mixed Integer Programmes, and outlines the main methods of solving them.

• Hardware
• algorithm
• algorithms
• combinatorics
• computer
• computer science
• linear optimization
• model
• modeling
• modelling
• nonlinear optimization
• operations research
• optimization
• programming
• scheduling

From the reviews:

"The book consists of a collection of self-contained chapters written by well-respected experts in the field. … the style of presentation is sufficiently uniform. … the editors formulate demonstration and communication of the pervasive nature of discrete optimization as their primary goal in producing this book. There are no doubts that they have achieved this goal." (Antanas Zilinskas, Interfaces, Vol. 38 (2), 2008)

• Operational Research Department, London School of Economics, UK

  Gautam Appa, H. Paul Williams

• Department of Mathematical and Physical Sciences, Aristotle University of Thessaloniki, Greece

  Leonidas Pitsoulis

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